In this paper we establish existence and regularity properties for the solutions of the variational model for Stress-Driven Rearrangement Instabilities (SDRI) [1]}, [2]}, [3]} that was introduced in [4]}. Under the name of Stress-Driven Rearrangement Instabilities are included all those
material morphologies, such as boundary irregularities, cracks, filaments, and surface patterns, which a crystalline material may exhibit in the presence of external forces, such as in particular the chemical bonding forces with adjacent materials. In order to release the induced stresses, atoms rearrange from the material optimal crystalline order and instabilities may develop.
